Spectral sensitivity in linear biological models

Properties of spectral components of the system matrix of linear time-invariant discrete or continuous models are investigated. It is shown that the entries in these matrices have the interpretation of being the sensitivity of the system matrix eigenvalues with respect to the model parameters. The spectral resolution formula for linear operators is used to get explicit results about component matrices and eigenvalue sensitivity. In biological modeling, particular interest is in the real maximal or minimal roots of the system matrix. Exact formulation of the related spectral components is made in important system matrix cases such as companion, Leslie, ecosystem, compartmental, and stochastic matrices.